A048049 - OEIS

%I #19 Sep 18 2022 12:36:53

%S 1,1,2,1,4,4,12,6,3,12,60,15,60,60,120,30,240,80,720,720,720,720,7920,

%T 7920,1584,1584,1584,1584,11088,11088,55440,13860,1386,11088,11088,

%U 11088,11088,11088,11088,5544,6930,13860,13860,3465,27720,27720,637560,1275120,182160

%N Denominator of Sum_{k=1..n} 1/phi(k).

%D József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Section I.27, page 29.

%H Robert Israel, <a href="/A048049/b048049.txt">Table of n, a(n) for n = 1..10000</a>

%H R. Sitaramachandrarao, <a href="https://www.jstor.org/stable/44236939">On an error term of Landau - II</a>, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientSummatoryFunction.html">Totient Summatory Function</a>.

%e 1, 2, 5/2, 3, 13/4, 15/4, 47/12, 25/6, 13/3, 55/12, 281/60, 74/15, ...

%p map(denom, ListTools:-PartialSums(map(1/numtheory:-phi, [$1..100]))); # _Robert Israel_, Apr 16 2019

%t Denominator[Accumulate[Table[1/EulerPhi[k], {k, 1, 50}]]] (* _Amiram Eldar_, Sep 18 2022 *)

%o (PARI) a(n) = denominator(sum(k=1, n, 1/eulerphi(k))); \\ _Michel Marcus_, Sep 18 2022

%Y Cf. A000010, A028415 (numerators).

%K nonn,frac

%O 1,3

%A _N. J. A. Sloane_, Jun 28 2002